objectives of section 9 - upatras eclass

Objectives of section 9

Write programs using linear interpolation to cut simple angles

Write simple programs using circular interpolation to mill arcs

3Slide

Linear interpolation:

Means cutting a straight line between two points

Sometimes this is referred to as a feedrate move since modern CNCcontrols automatically perform linear interpolation on any move made whilein feedrate mode

Prior to modern CNC controls special codes were necessary to turn on thebuilt-in linear interpolation system

Some CNC controls also will interpolate rapid moves - while others simplymove the axes drive motors at maximum speed in rapid traverse mode

Linear Interpolation

4Slide


The axis the spindle moves with basic orthogonal movements from thebeginning to the end of the path

The programmed rectilinear path is divided into a large number of shortlength straight lines

The more lines, the better approximation is made of the actual path

The more lines, the more computational power required - No longer used fornon straight segments

5Slide

Linear interpolation:

Machines capable of linear interpolation have a continuous-path controlsystem - meaning that the drive motors on the various axes can operate atvarying rates of speed

Virtually all modern CNC controls utilize continuous path controls

When cutting an angle the MCU calculates the angle based on theprogrammed coordinates

Since the MCU knows the current spindle location, it can calculate thedifference in the X coordinate between the current position and theprogrammed location

The change in the Y coordinate divided by the change in the X coordinate yields the slope of the cutter centerline path


6Slide


Interpolating in Word Address Format

Milling an angle with word address is not complicated

The interpolator is automatically turned on when feedrate mode iscommanded

Milling becomes a matter of specifying the coordinates along with the G01feedrate mode code

In CNC shops G01 is called: the feedrate mode code or the linearinterpolation code

With modern CNC controls the terms mean the same thing

Any feedrate move is considered an interpolated angled line move

A move along the X axis only would cut an angled line of 0 degrees

A move along the Y axis would cut an angle of 90 degrees

7Slide

Notes Linear interpolation is not difficult

Aside from calculating the cutter offsets necessary to position the spindle - it is the same asstraight line milling

The real difference is that an X and a Y coordinate are specified for the ending point of theangle since there is a change in position of both axes

Other cutter situations will present themselves in CNC part programming such as arcs tangentto an angle or arcs tangent to other arcs

CAM programming systems automatically calculate cutter offsets with speed and accuracyno programmer can match

For this reason CAM systems have become the preferred programming system in many shops

A good programmer or CNC operator must still know how to calculate cutter offsets in order toedit programs in the machine control during the first piece setup

8Slide


Other cutter situations will present themselves in CNC part programmingsuch as arcs tangent to an angle or arcs tangent to other arcs

CAM programming systems automatically calculate cutter offsets withspeed and accuracy no programmer can match

For this reason CAM systems have become the preferred programmingsystem in many shops

A good programmer or CNC operator must still know how to calculatecutter offsets in order to edit programs in the machine control during thefirst piece setup

9Slide

Circular Interpolation

In cutting arcs, the MCU uses its ability to generate angles to approxi-mate an arc

Since the machine axes do not revolve around a centerpoint in a typicalthree-axis arrangement, the cutting of a true arc is not possible

Circular interpolation is the term used to describe generating a move con-sisting of a series of straight-line chord segments by the MCU in twoaxes to simulate circular motion

These chord segments are very small and practically indistinguishable froma true arc

10Slide

Limited to the main plane of the machined surface

Unable participation of the rotary machining axis of the machine-tool

Not used for interpolation in the space due to requirement of the combinedmovement of three or more machining axes

Ideal for moving the axes when the path of the cutting tool in a planecontains circles, half circles or arcs. In this case only the coordinates of theends of the arc, the radius and center are required


11Slide


Specifying Axis for Interpolation

G17 – Selects the X/Y plane (X and Y axis) G18 – Selects the Y/Z plane (Y and Z axis) G19 – Selects the Z/X plane (Z and X axis)

Circular interpolation by definition involves only two axes. On FANUC-style controls, a plane designation code is used to select which pair of

axis will be used to generate the arc motion. There are three G codes used to specify these planes:

These G codes are modal. A G17, for example, is cancelled only by a G18 or G19

The X/Y plane (using the X and Y axis) is the most common orientation for circularinterpolation, therefore, G17 will be used throughout the examples in this text

12Slide


Specifying Arc Direction

G02 – Circular interpolation clockwise (CLW) G03 – Circular interpolation counterclockwise (CCLW)

Circular interpolation can be accomplished in one of two directions: clockwise, orcounterclockwise. There are two G codes used to specify direction.

G02/G03 codes are modal They will cancel an active G00 (rapid traverse) or G01 (linear interpolation) codes G02/G03 are feedrate mode codes, just as G01 is. The difference lies in the type of interpolation used. G01 generates straight-line interpolation motion. G02/G03 generates arc simulation

interpolation motion

13Slide

Specifying Beginning and Ending Arc Coordinates

The MCU requires the spindle be positioned at the start of the arc when the G02/G03command is given

The current spindle position is the beginning arc coordinates. The axis coordinatesgiven on the G02/G03 line are the spindle ending points of the arc motion

Specifying Arc Center points

There are two methods used to specify arc centerpoints: arc vector method andradius method (see Figure 9-8)

The arc vector method involves specifying the coordinates of the arc centerpoint asX/Y values

In the radius method, the arc centerpoint is calculated internally by the MCU. Theprogrammer simply specifies the radius value required


14Slide


Arc Vector Method

Since X, Y, and Z addresses are used to specify the end point of an arc,secondary addresses are required to specify the centerpoint of an arc. Thefollowing addresses are used to designate arc center points

I—X-axis coordinate of an arc. J—Y-axis coordinate of an arc. K—Z-axis coordinateof an arc

Since circular interpolation occurs only in two axes, only two of these three codeswill be required to generate an arc. When using the X/Y plane for milling arcs, as thistext does, the I and J addresses are used

The different ways controllers required the arc centerpoints to be specifiedcomplicate this matter: absolute coordinates, to circle center, or from circlecenter. FANUC-style controls usually utilize the to circle center method

15Slide


Absolute Coordinates

Some controls require the arc centerpoints specified by I, J, and/or K be theposition of the arc center relative to the coordinate system origin

In other words, the center of the arc is specified just as if it were a cuttercoordinate using absolute positioning

IF the arc centerpoints are at X2.000, Y2.000. They would be specified as12.0000 J2.0000 as in the following circular interpolation block:

N120 G17 G02 X3. Y2. 12. J2. F7

16Slide

Although the radius method is easier to use than the arc vector method, the

latter method is still common

This is most likely because the radius method became available only with

the advent of modern CNC controllers

Many of today's programming practices have ties to the tape-controlled

MCU of days gone by. This use of the arc vector method is one of these


17Slide


N001 G80 G90 G00 G98N100 T01 M06N101 G00 X-0.25 Y-0.25N102 G44 Z-1. H01N103 G01 Y3N104 X2.N105 G17 G02 X3. Y2. I2. J-1. F7.2N106 G01 Y-0.25N107 X-0.25N108 G00Z0N109 G49N110 G91 G28 X0. Y0. Z0.N110 M01

(optional stop code)(rapid to home zero)(cancel tool offset)(retract Z)(feed #5 to #1)(feed #4 to #5)(circular move to #4)(feed #2 to #3)(feed #1 to #2)(tool offset pickup)(rapid to #1)(tool change block)(safety block)

This example is typical of FANUC, General Numeric, and other FANUC- style controls:

18Slide

N001 G80 G90 G00 G98N100 T01 M06N101 G00 X-0.25 Y-0.25N102 G44 Z-1. H01N103 G01 Y3N104 X2.N105 G17 G02 X3. Y2. I2. J-1. F7.2N106 G01 Y-0.25N107 X-0.25N108 G00Z0N109 G49N110 G91 G28 X0. Y0. Z0.N110 M01


The following code uses the from circle center method to specify arc centerpoints:


19Slide


Radius Method

N001 G80 G90 G00 G98N100 T01 M06N101 G00 X-0.25 Y-0.25N102 G44 Z-1. H01N103 G01 Y3N104 X2.N105 G17 G02 X3. Y2. R1. F7.2N106 G01 Y-0.25N107 X-0.25N108 G00Z0N109 G49N110 G91 G28 X0. Y0. Z0.N110 M01

The following code mills the part using the radius method of specifying arc center coordinate:


20Slide


Additional Circular Interpolation Examples

The programs just discussed deal with simple arcs which intersect a lineparallel to a machine axis

In many cases, however, an arc will intersect an angle or another arc

The cutter offsets for these situations can be found by using the formulas

21Slide

Summary 1/3

Linear interpolation is the ability to cut angles. It is simply a feedrate move,in a straight line, between two points

Circular interpolation is the ability to cut arcs or arc segments. Arcs arecut by means of a series of choral segments generated by the MCU toapproximate the arc curvature

It is necessary to calculate the cutter offset coordinates when using linearand circular interpolation

G01 is the code to institute linear interpolation. It also is referred to as thefeedrate move code

G02 and G03 are used to institute circular interpolation

22Slide

Summary 2/3 G02 turns on clockwise interpolation. G03 turns on counterclockwise interpolation

There are two methods used to specify the arc center-points to the MCU: the arcvector method and the radius method

When using the arc vector to specify center-points, some controls require thecenter-points to be given in absolute coordinates, some in incrementalcoordinates from the cutter center to the circle center, and other in incrementalcoordinates from the circle center to the cutter center

The format for circular interpolation for the arc vector method is:

G17 G02G18 G03 X… Y… Z… I… J… K…

G19

For most uses (X/Y plane interpolation) the format is:G17 G02/G03 X… Y… I… J…

23Slide

Summary 3/3

The format for circular interpolation for the radius method is:

G17 G02G18 G03 X… Y… Z… R…G19

For most uses (X/Y plane interpolation) the format is:

G17 G02/G03 X… Y… R…

24Slide

Vocabulary Introduced in this section Arc center-points

Arc vector method

Circular interpolation

From circle center

Linear interpolation

Radius method

To circle center

25Slide

End of Section

Reference NoteCopyright University of Patras, School of Engineering, Dept. ofMechanical Engineering & Aeronautics, Dimitris Mourtzis. DimitrisMourtzis. «Computer Numerical Control of Machine Tools. Linear andCircular Interpolation». Version: 1.0. Patras 2015. Available at:https://eclass.upatras.gr/courses/MECH1213/

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objectives of section 9 - upatras eclass

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